Question

How is the volume of a cylinder affected when its radius is doubled?

Answer 1

Volume quadrupled.

Explanation:

`V_("cylinder") = pir_("cylinder")^2h`

`therefore V prop r^2 implies V = kr^2`

Let `r_2 = 2r_1`, then

`V_2/V_1 = (kr_2^2)/(kr_1^2) = r_2^2/r_1^2`

`V_2 = V_1(r_2/r_1)^2 = V_1((2r_1)/(r_1))^2 = V_1(2)^2 = 4V_1`